Create a modal line or benchmark

Question

I have some data the following, X is cycle in percentage, and Y is the quantity:

SampleID　X　　　　Y
1　　　　　0.52　　0.9720
1　　　　　0.66　　0.9760
1　　　　　0.67　　0.9760
1　　　　　0.69　　0.9952
2　　　　　0.21　　0.2564
...

And I tried to average the Y with same X value, such that I can draw a chart like this:

Here is the data file: Link to Google Drive

This chart not very ideal, I want to create a chart more like a curve, so that I may able to compare with other sample data. But my problem is, I'm not sure what technique I should use, is there have any suggestion? I tried the linear regression, but not what I want, maybe I should have something like sigmoid?

Answer 1

It seems that a quarter cycle occurs for every 0.88 of x. In addition y ranges from 0 to 1.00 approx. So you can try fitting $$ y(x) = Y \left( \frac{1}{2} - \frac{\cos(\pi x/a)}{2} \right) $$